Question

Which one of the following represents simple harmonic motion?

• A. $\text{Acceleration}=-{\mathrm{k}}_0\mathrm{x}+{\mathrm{k}}_1{\mathrm{x}}^2$
• B. $-\mathrm{k}\left(\mathrm{x}+\mathrm{a}\right)$
• C. $\mathrm{k}\left(\mathrm{x}+\mathrm{a}\right)$
• D. $\mathrm{kx}$

Answer 1

The correct option is B

$-\mathrm{k}\left(\mathrm{x}+\mathrm{a}\right)$

The explanation of the correct option (D):

Simple harmonic motion:

The equation for acceleration in SHM is given by $a=\left(-\frac{k}{m}\right)x$

The explanation for the incorrect options:

1. Since option (c) and option (d) have positive values for acceleration they are incorrect.
2. $a\propto x$ therefore option (a) is also incorrect.

Hence, Option(B) is correct.